 16.6.1: 12 Determine whether the points and lie on the given surface.ru, v ...
 16.6.2: 12 Determine whether the points and lie on the given surface.ru, v ...
 16.6.3: 36 Identify the surface with the given vector equation.ru, v u v i ...
 16.6.4: 36 Identify the surface with the given vector equation.ru, v 2 sin ...
 16.6.5: 36 Identify the surface with the given vector equation.rs, t s, t, ...
 16.6.6: 36 Identify the surface with the given vector equation.rs, t s sin ...
 16.6.7: 712 Use a computer to graph the parametric surface. Get a printout ...
 16.6.8: 712 Use a computer to graph the parametric surface. Get a printout ...
 16.6.9: 712 Use a computer to graph the parametric surface. Get a printout ...
 16.6.10: 712 Use a computer to graph the parametric surface. Get a printout ...
 16.6.11: 712 Use a computer to graph the parametric surface. Get a printout ...
 16.6.12: 712 Use a computer to graph the parametric surface. Get a printout ...
 16.6.13: 1318 Match the equations with the graphs labeled IVI and give reaso...
 16.6.14: 1318 Match the equations with the graphs labeled IVI and give reaso...
 16.6.15: 1318 Match the equations with the graphs labeled IVI and give reaso...
 16.6.16: 1318 Match the equations with the graphs labeled IVI and give reaso...
 16.6.17: 1318 Match the equations with the graphs labeled IVI and give reaso...
 16.6.18: 1318 Match the equations with the graphs labeled IVI and give reaso...
 16.6.19: 1926 Find a parametric representation for the surface.The plane thr...
 16.6.20: 1926 Find a parametric representation for the surface.The plane tha...
 16.6.21: 1926 Find a parametric representation for the surface.The part of t...
 16.6.22: 1926 Find a parametric representation for the surface.The part of t...
 16.6.23: 1926 Find a parametric representation for the surface.The part of t...
 16.6.24: 1926 Find a parametric representation for the surface.The part of t...
 16.6.25: 1926 Find a parametric representation for the surface.The part of t...
 16.6.26: 1926 Find a parametric representation for the surface.The part of t...
 16.6.27: 2728 Use a computer algebra system to produce a graph that looks li...
 16.6.28: 2728 Use a computer algebra system to produce a graph that looks li...
 16.6.29: Find parametric equations for the surface obtained by rotating the ...
 16.6.30: Find parametric equations for the surface obtained by rotating the ...
 16.6.31: (a) What happens to the spiral tube in Example 2 (see Fig ure 5) if...
 16.6.32: The surface with parametric equations where and , is called a Mbius...
 16.6.33: 3336 Find an equation of the tangent plane to the given parametric ...
 16.6.34: 3336 Find an equation of the tangent plane to the given parametric ...
 16.6.35: 3336 Find an equation of the tangent plane to the given parametric ...
 16.6.36: 3336 Find an equation of the tangent plane to the given parametric ...
 16.6.37: 3738 Find an equation of the tangent plane to the given parametric ...
 16.6.38: 3738 Find an equation of the tangent plane to the given parametric ...
 16.6.39: 3950 Find the area of the surface.The part of the plane that lies i...
 16.6.40: 3950 Find the area of the surface.The part of the plane with vector...
 16.6.41: 3950 Find the area of the surface.The part of the plane that lies i...
 16.6.42: 3950 Find the area of the surface.The part of the cone that lies be...
 16.6.43: 3950 Find the area of the surface.The surface ,z 23 x 32 y 32 0 x 1...
 16.6.44: 3950 Find the area of the surface.The part of the surface z 1 3x 2y...
 16.6.45: 3950 Find the area of the surface.The part of the surface that lies...
 16.6.46: 3950 Find the area of the surface.The part of the paraboloid that l...
 16.6.47: 3950 Find the area of the surface.The part of the surface that lies...
 16.6.48: 3950 Find the area of the surface.The helicoid (or spiral ramp) wit...
 16.6.49: 3950 Find the area of the surface.The surface with parametric equat...
 16.6.50: 3950 Find the area of the surface.The part of the sphere that lies ...
 16.6.51: If the equation of a surface is , where , and you know that and , w...
 16.6.52: 5253 Find the area of the surface correct to four decimal places by...
 16.6.53: 5253 Find the area of the surface correct to four decimal places by...
 16.6.54: Find, to four decimal places, the area of the part of the surface t...
 16.6.55: (a) Use the Midpoint Rule for double integrals (see Sec  tion 15.1...
 16.6.56: Find the area of the surface with vector equation , , . State your ...
 16.6.57: Find the exact area of the surface , , .
 16.6.58: (a) Set up, but do not evaluate, a double integral for the area of ...
 16.6.59: . (a) Show that the parametric equations , , , , , represent an ell...
 16.6.60: (a) Show that the parametric equations , , , represent a hyperboloi...
 16.6.61: Find the area of the part of the sphere that lies inside the parabo...
 16.6.62: The figure shows the surface created when the cylinder intersects t...
 16.6.63: Find the area of the part of the sphere that lies inside the cylinder
 16.6.64: (a) Find a parametric representation for the torus obtained by rota...
Solutions for Chapter 16.6: Parametric Surfaces and Their Areas
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 16.6: Parametric Surfaces and Their Areas
Get Full SolutionsSince 64 problems in chapter 16.6: Parametric Surfaces and Their Areas have been answered, more than 29762 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. Chapter 16.6: Parametric Surfaces and Their Areas includes 64 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Bar chart
A rectangular graphical display of categorical data.

Bearing
Measure of the clockwise angle that the line of travel makes with due north

Binomial coefficients
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n  r2!

Cotangent
The function y = cot x

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Multiplicative inverse of a matrix
See Inverse of a matrix

Partial fraction decomposition
See Partial fractions.

Polar equation
An equation in r and ?.

Positive numbers
Real numbers shown to the right of the origin on a number line.

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Projectile motion
The movement of an object that is subject only to the force of gravity

Range (in statistics)
The difference between the greatest and least values in a data set.

Regression model
An equation found by regression and which can be used to predict unknown values.

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

Vertical stretch or shrink
See Stretch, Shrink.